For 1, consider an infinitely small change in theta (or, mathematical, the derivative): The energy must not change, so the derivative is 0.Moving the left fluid up (left side of the first hint) costs the same energy as moving the other fluid down (right side) gives.The other lines are just steps to get an expression theta=... based on that.

For 2: The diagonal springs are treated as effective springs with a different constant k', based on the force they apply when the mass goes up/down.

Caution: I am a biologist with limited knowledge of physics, so I may be totally wrong. I intuitively think the term comes into play by combining the force vector from the two springs that are at a 135 degree angle to the downward springs. Combining those two vectors ultimately simplifies the whole system to just two springs, each exerting a force in opposite directions.

Caution: I am a biologist with limited knowledge of physics, so I may be totally wrong. I intuitively think the term comes into play by combining the force vector from the two springs that are at a 135 degree angle to the downward springs. Combining those two vectors ultimately simplifies the whole system to just two springs, each exerting a force in opposite directions.

So basically, when each spring is compressed, it exerts a force back. How much do the springs at an angle get compressed when you displace the particle straight up? What is the component of the force the springs exert along the vertical direction?

If it is homework/coursework, Afif_D, have you already talked with your professor/teacher about these problems? If not, why not? They should be your first recourse for any questions you have; that's what they're there for. If you have already asked them about these problems, what about their explanations was unsatisfactory? Note that just giving you the exact detailed solution hardly ever lets you learn much. Trying to work it out for yourself with some hints is usually much better for gaining actual understanding.

starslayer wrote:If it is homework/coursework, Afif_D, have you already talked with your professor/teacher about these problems? If not, why not? They should be your first recourse for any questions you have; that's what they're there for. If you have already asked them about these problems, what about their explanations was unsatisfactory? Note that just giving you the exact detailed solution hardly ever lets you learn much. Trying to work it out for yourself with some hints is usually much better for gaining actual understanding.

Coz our school is closed. I have been trying to figure out how these two things come up

Did my advice help you? I got caught on where the cos2 came from too, and I think the problem is that once you write F = kx y = 2k cos(45) y, you are treating the two springs as a single vertical one.The thing is, when the particle moves y in the vertical direction, how much of that is compressing the springs?

cemper93 wrote:Dude, I just presented an elaborate multiple fraction in Comic Sans. Who are you to question me?

Afif_D wrote:Coz our school is closed. I have been trying to figure out how these two things come up

They come up because physics-literate forums see this kind of thing all the time. Some people will just post their homework and ask for the answer, without mentioning that it's homework. Since you say this isn't homework, great. It still doesn't mean that presenting you with the solution in its entirety would be all that helpful to you for understanding the principles behind the solutions. Hints like the ones given are much better for that, especially since you already know what the answers are and can easily check your work.

To be fair, in this case the solution is basicly provided along with the problem with essentially all the work (although I can't seem to display it all), making it more likely to be review material rather then any form of homework, it's just the justification for each step that's missing.

The cos^2 bit is sneaky, but if you think of it as two seperate cos's (one nestled with the x, and one with the overall force) it works out I believe. I haven't looked at it too closely though since the full thing is cut off for me.

Dopefish wrote:To be fair, in this case the solution is basicly provided along with the problem with essentially all the work (although I can't seem to display it all), making it more likely to be review material rather then any form of homework, it's just the justification for each step that's missing.

The cos^2 bit is sneaky, but if you think of it as two seperate cos's (one nestled with the x, and one with the overall force) it works out I believe. I haven't looked at it too closely though since the full thing is cut off for me.

Point taken, however, the most the important parts of the solution aren't. For example, the first problem is all about getting the first expression (I haven't figured it out yet, but I haven't thought about it all that hard), and the rest is gravy.

To view the whole problem, right click the image and select "view image."